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Implications of Relativistically Consistent Wave Function Collapse

Allan Goff, Dale Lehmann, Joel Siegel

Published Jul 9, 2006• 7 citations

Abstract

In the current formalism of quantum mechanics, collapse of the wave function is envisioned as occurring “instantaneously”. Since this is in conflict with the fact that “simultaneity” is not a relativistic invariant, quantum mechanics and relativity are in conflict with each another. This conflict is benign as long as faster-than-light (FTL) phenomena are disallowed. This paper explores this conflict and considers the implications if collapse can be specified to occur in a way that is consistent with relativity. In particular, relativistically consistent wave function collapse forces us to reconsider our preconceptions of causality. We are led to consider two cases; timelike and spacelike. For two events that are causally connected by a timelike interval, the earlier-in-time event is the cause in all reference frames, but the spatial ordering is not preserved. For two events that are causally connected by a spacelike interval, the temporal ordering is not preserved but the spatial ordering is, just the reverse. This is philosophically disturbing since for spacelike causes half the reference frames see the cause as proceeding backwards in time. However, in and of itself this is not logically inconsistent. Backwards-in-Time Causality (BTC) seems at first glance to permit temporal paradox, since two spacelike causal connections can be used to create a closed causal loop in spacetime. While temporal paradox is logically inconsistent, BTC can still be allowed if there is also a censor mechanism that prevents temporal paradox. In relativity, FTL and BTC are two sides of the same coin, so the major implication of relativistically consistent wave function collapse is that quantum systems should be able to support both FTL and BTC phenomena despite Eberhard’s “proof.”

DOI: 10.2514/6.2006-4729

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